Week 3 of the 2016 #MTBoS Blogging Initiative
By "better questions" we might mean - Pose good questions in class. Mathematical questions that are cognitively demanding and make students think. By "better questions" we might also mean - Question students in a way that is not cognitively funneling or draining students of the opportunity to think. Pose questions that matter and incite classroom discourse. In other do this we may need frameworks for good problems/questions to pose or frameworks for good questions. My favorites: For using cognitively demanding tasks, check out Smith and Stein's framework here or in the Principles to Action. For a framework for talking about questions more, you can check out Connecting Mathematical Ideas (see, e.g., Border problem chapter) and can also look at the Principles to Action.
Meanwhile, this blog post is coming a bit late because the later part of my week last week I was at a conference - AMTE. While at the conference, I thought about the opportunity of asking other teachers questions and other researchers questions. What does it mean to question our research or to pose questions that make others reflect on their research? What does it mean to question the ways you design tasks or pose question.
When better questioning is questioning yourself and the things you do...
Questioning my research.
One of my favorite talks at AMTE was Eva Thanheiser's Award Talk. During her talk, she shared her 7-year journey in the field and how her research agenda evolved. She discussed how she was first interested in prospective teachers' conceptions about whole number and operations and how that interested transitioned into an interest in investigating how we motivate prospective teachers' to learn about number. Listening to her talk, which included 7 years of data from elementary prospective teachers' in content and methods courses, prompted me to think about my own research. I study the ways that children think about negative number and the ways that prospective teachers thinking about negative number. While that is important, why do I do that? What is the larger purpose to study that. Right now (in year 1 of my journey), I think I study how children think about negative number to tell a story about how powerful their reasoning is and how it is different from how we support learning of negative number currently. I study how prospective teachers think about negative number so that I can better understand what they know and do not know in order that I may create tasks to support their learning and development of Mathematical Knowledge for Teaching.
Questioning my teaching.
My other favorite session at AMTE was a session on complex instruction. Some of the authors of Smarter Together! and others presented their experiences of taking a task and making is "complex instruction" worthy. They joked that they were "CI-ing" tasks. During this session, we were encouraged and facilitated to take a task and "CI" it. Working collaboratively with some new colleagues, we took a task and attempted to incorporate ways that supported the involvement of all students and contained opportunities for different ways of "smartness" to be represented: Solving in a task in multiple ways, drawing visual representations, providing opportunities for creativity, etc. And, I thought: What if I did this more? What if I took the opportunity to intentionally make an ordinary task complex instruction worthy more than in this session? And, what stops me from doing this (e.g., intentionally modifying tasks to support complex instruction) more? My first response to questioning myself was - it is time consuming to do and that is why I have not done it more. However, I found that a poor excuse because with collaboration we were table to "CI" an existing task well and about a half hour. I am definitely motivated to utilizing complex instruction more. And, I left the session questioning myself about how I might integrate complex instruction more.